Our method for classifying nilpotent bicommutative algebras is based on the calculation of central extensions of smaller nilpotent algebras from the same variety.
The algebraic study of central extensions of Lie and non-Lie algebras has been an important topic for years [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, especially due to their usefulness to classify nilpotent algebras from different varieties.
First, Skjelbred and Sund employed central extensions of Lie algebras to obtain a classification of nilpotent Lie algebras [5]}.
After that, and basing on the method developed by Skjelbred and Sund, all non-Lie central extensions of all 4-dimensional Malcev algebras were described [3]},
all anticommutative central extensions of 3-dimensional anticommutative algebras [10]},
and all central extensions of 2-dimensional algebras [11]}.
Also, central extensions were used to give classifications of
4-dimensional nilpotent associative algebras [12]},
5-dimensional nilpotent Jordan algebras [13]},
5-dimensional nilpotent restricted Lie algebras [14]},
5-dimensional nilpotent associative commutative algebras [15]},
6-dimensional nilpotent Lie algebras [16]}, [17]},
6-dimensional nilpotent Malcev algebras [18]},
6-dimensional nilpotent anticommutative algebras [19]},
8-dimensional dual Mock Lie algebras [20]},
and some others.
